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Keywords:

  • biodiversity effect;
  • BIOTREE ;
  • carbon isotope composition;
  • complementarity effect;
  • FunDivEUROPE;
  • method;
  • selection effect;
  • water use efficiency

Summary

  1. Top of page
  2. Summary
  3. Introduction
  4. Application of Loreau & Hector's (2001) method to complex functional traits
  5. Application of the modified equations to ecosystem-level carbon isotope composition
  6. Materials
  7. Results and discussion
  8. Conclusion
  9. Acknowledgements
  10. Author contributions
  11. References
  1. In 2001, Loreau and Hector proposed a method to calculate the effect of biodiversity on ecosystem-level properties that distinguished selection effects (SE) from complementarity effects (CE). The approach was designed and has been widely used for the study of yield in mixed-species situations taking into account the relative abundance of each species in ecosystem-level yield. However, complex functional traits commonly used to integrate ecosystem-level properties that cannot be analysed like yield data because the weighted contribution of each species is not determined by its relative abundance.
  2. We adapted the original method by clearly identifying ecologically meaningful weighting coefficients to represent species-specific contributions to ecosystem function.
  3. We applied the adapted method of analysis to tree foliar carbon isotope composition in an experimental plantation in order to test the influence of species richness on plot water use efficiency (WUEplot). The appropriate weights for the WUEplot of each species are leaf CO2 assimilation rate.
  4. We observed a large range of WUEplot and biodiversity effects among plots. The absence of a significant SE on WUEplot indicated that the overall net biodiversity effect was primarily driven by a CE. The net biodiversity effect and CE were mostly negative, suggesting that interspecific interactions resulted in a decrease in the ratio between carbon acquisition and transpiration at the ecosystem level.
  5. The application of the method to complex components of ecosystem functioning provides important new insights into the practical and conceptual aspects of functional biodiversity research.

Introduction

  1. Top of page
  2. Summary
  3. Introduction
  4. Application of Loreau & Hector's (2001) method to complex functional traits
  5. Application of the modified equations to ecosystem-level carbon isotope composition
  6. Materials
  7. Results and discussion
  8. Conclusion
  9. Acknowledgements
  10. Author contributions
  11. References

The loss of biodiversity occurring in most natural environments world-wide has sparked an interest among the scientific community in the relationship between biodiversity and ecosystem functioning (Hooper et al. 2012). More than 20 years of ecological studies have led to a consensus that ecosystem performance is highly dependent on species richness and on species functional characteristics (Loreau et al. 2001; Hooper et al. 2005; Zhang, Chen & Reich 2012). However, the mechanisms underlying biodiversity–function relationships have been hotly debated. Two major groups of mechanisms were initially proposed to explain positive effects of biodiversity: (i) a sampling or selection effect (SE) which arises, as species richness increases, from the increasingly probable occurrence of one or several species that strongly contribute to the ecosystem function observed (Aarssen 1997; Huston 1997; Tilman 1997), and (ii) a complementarity effect (CE) driven either by niche differentiation among species, which tends to increase the efficiency with which coexisting species use the available resources or to facilitation or other mutualistic interactions among species (Tilman et al. 1997; Loreau 1998). Recently, the combination of evenness, richness and life-history variations was also successfully linked to the mechanisms producing positive biodiversity effects (Zhang, Chen & Reich 2012).

To quantitatively evaluate this biodiversity – ecosystem functioning relationship and partition the underlying mechanisms, Loreau & Hector (2001) proposed a convenient method to calculate the influence of species mixture on ecosystem productivity: the net biodiversity effect on the yield (ΔY) of a given mixture can be calculated as the difference between the observed total yield in the mixture (YO) and the expected total yield in the mixture (YE) under the null hypothesis that intraspecific and interspecific interactions are identical. The original method was extended by Fox (2005) to include trait-dependent and trait-independent CE in addition to the dominance effect (tripartite partitioning).

Loreau and Hector's method has been widely used and so far more than 100 peer-reviewed papers analysing the relationships between species richness and ecosystem functioning in highly diverse biomes have been published. Even though the method has proven to be very popular, existing studies have focused on a limited number of ecosystem functions, mostly on standing biomass.

One explanation for this limited application could stem from the fact that some ecological functions in mixed species stands cannot be treated at the ecosystem level in the same way as observed yield. For complex functional properties, ecosystem-level values correspond to the mean value of the species present in the community weighted by the contribution of each species to the given function; this weighted contribution can be totally different from the relative abundance of these species in terms of frequency or biomass, which the original method does not imply. These complex functions include, among others, any measurement related to the efficiency of individuals to acquire and use resources (e.g. water use efficiency, photosynthesis efficiency, nutrient use efficiency), whatever the ecosystem (plant or aquatic ecosystems, bacterial communities…). The isotope composition of organic or mineral elements in biological material or the density of any gas flux (e.g. sap flow density, density of CO2 respiration) is also an example of such complex functional traits.

In this paper, we extend Loreau & Hector's (2001) method to complex functional traits by clearly identifying ecologically meaningful weighting coefficients, which represent species-specific contributions to ecosystem functioning. We illustrate the usefulness of the adapted equations for leaf carbon isotope composition. More precisely, we analyse the effect of species richness on foliar carbon isotope composition (δ13C) at the ecosystem level in a temperate mixed-species tree plantation. Foliar δ13C is a convenient proxy for time-integrated intrinsic water use efficiency (WUEint; Farquhar, O'Leary & Berry 1982) and reflects the trade-off between CO2 acquisition and stomatal regulation of transpiration at the leaf level. Foliar δ13C and WUEint can only be obtained at the individual level, and ecosystem-level δ13C cannot be calculated by simply taking into account the summed contribution of the individuals in terms of biomass or frequency. Instead, the proportional amount of CO2 assimilated by each species in the plot needs to be considered to correctly weight each species' contribution to ecosystem-level functioning.

Application of Loreau & Hector's (2001) method to complex functional traits

  1. Top of page
  2. Summary
  3. Introduction
  4. Application of Loreau & Hector's (2001) method to complex functional traits
  5. Application of the modified equations to ecosystem-level carbon isotope composition
  6. Materials
  7. Results and discussion
  8. Conclusion
  9. Acknowledgements
  10. Author contributions
  11. References

According to Loreau & Hector (2001), the net biodiversity effect on the yield (ΔY) of a given mixture of species is the difference between the observed total yield in the mixture (YO) and the expected total yield in the mixture (YE) calculated as the sum of the products between the yield of the different species in their corresponding monocultures and the proportion of the species in the mixture (defined in terms of individual frequency or biomass):

  • display math(eqn 1)

where N is the number of species in the mixture, YOi and YEi denote the observed and expected yield of species i in the mixture, Mi is yield of species i in the monoculture, RYOi is the observed relative yield of species i in the mixture and RYEi is the expected relative yield of species i in the mixture. RYOi is calculated as the ratio of the observed yield of species i in the mixture and the yield of species i in the monoculture, whereas RYEi is simply the proportion of species i seeded or planted in the mixture.

For complex functional properties where the contribution of each species to a given ecosystem-level function is not simply proportionate to the frequency of these species or their proportion in biomass, we introduce a weighting coefficient (WOi) to calculate the contribution of species i to the complex function (F) in the mixed plots. WOi is normalised to one and therefore represents a proportional contribution. Thus, the net biodiversity effect on a complex function (ΔF) is written as:

  • display math(eqn 2)

where FOi and FEi denote the observed and expected value of the function of species i in the mixture. This equation is a generalisation of the equation proposed by Loreau & Hector (2001). If one considers that FOi is the observed biomass of species i in the mixed plot and WOi is the proportion of species i in the mixed plot in terms of the number of seeded individuals or in terms of biomass, then FOi × WOi equals YOi. Similarly, if one considers that FEi is the observed biomass of species i in the monoculture and WOi is the proportion of species i in the mixed plot in terms of the number of seeded individuals or in terms of biomass, then FEi × WOi equals YEi.

The weighting coefficients are specific to each studied complex property and must take into account the underlying biological and ecological mechanisms to correctly estimate the contribution of each species to ecosystem-level functioning. In Table 1, we have listed some weighting factors that could be used in plant ecological studies. Let us illustrate this point with sap flow density. Sap flow density (Lsap inline image per h) represents the density of the flow of raw sap circulating in the xylem vessels of trees and can be directly measured with sap flow sensors at the single tree level. However, sap flow density cannot simply be added among the trees to calculate total plot sap flow density and to estimate the influence of biodiversity on this ecosystem-level property, because the proportion in biomass or tree frequency among species in the mixture does not give the proportional contribution of each species to total plot sap flow density. Rather, sapwood area (the cross-sectional, water conducting area in the trunk) of each tree is the correct weighting coefficient and should be used as the quantity WOi in eqn (eqn 2).

Table 1. Examples of complex functional properties used in plant ecological studies, with units and suitable corresponding weighting coefficients
PropertiesUnitsWeighting coefficient
Sap flow densityL dm−2 per hSapwood area
Bark CO2 effluxμmol m−2 per sTrunk surface
Photosynthesisμmol m−2 per sLeaf area
Leaf water use efficiencyμmol mol−1Leaf CO2 exchange
Carbon isotope compositionLeaf CO2 exchange
Plant water use efficiencykg L−1Leaf area
Nutrient uptake ratesμmol g−1 per hRoot surface area

The goal of Loreau & Hector's (2001) method is to partition ΔY into two effects generated by species interactions in mixtures: SE and CE. SE arises from interspecific competition leading to the dominance of a given species with particular functional traits. CE reflects the degree to which niche differences and facilitation outweigh interference competition and other negative species interactions (Loreau et al. 2012). As when calculating ΔY, partitioning the effects of complex functions into SE and CE must also take WOi into account. The equation to calculate CE can be rewritten as:

  • display math(eqn 3)

and the equation for SE is:

  • display math(eqn 4)

As our approach is intended to be a generalisation of the original method and can be applied to complex functions, which are not directly related to yield, changes in species contribution with time are not taken into account in eqn (eqn 4). The SE thus here stresses the dominance of a one or more species for the considered complex ecosystem function at a given time.

Application of the modified equations to ecosystem-level carbon isotope composition

  1. Top of page
  2. Summary
  3. Introduction
  4. Application of Loreau & Hector's (2001) method to complex functional traits
  5. Application of the modified equations to ecosystem-level carbon isotope composition
  6. Materials
  7. Results and discussion
  8. Conclusion
  9. Acknowledgements
  10. Author contributions
  11. References

A positive effect of species mixture on forest ecosystem productivity (Paquette & Messier 2011; Zhang, Chen & Reich 2012) and transpiration (Forrester et al. 2010; Kunert et al. 2012) has previously been reported. Complementarity effects and SE for these ecosystem-level parameters were highlighted with Loreau & Hector's (2001) method, thus making it possible to explain differences in ecosystem functioning among species richness levels. Promoting a mixture of tree species to enhance the ratio of ecosystem-level productivity to transpiration (i.e. high water use efficiency) has been advocated for sustainable forest management (McCarthy et al. 2011), of particular importance in a context of climate change. To further investigate this relationship, we applied the widely used carbon isotope approach (Farquhar, O'Leary & Berry 1982) to study the impact of tree species mixtures on ecosystem-level water use efficiency (WUEplot) in a temperate mixed plantation.

At leaf level, intrinsic water use efficiency (WUEint) represents the ratio between photosynthetic assimilation of CO2 by the leaf (A) and stomatal conductance for water vapour (gs) and depends on the molar fraction of CO2 in the air (Ca) and in the leaf intercellular spaces (Ci) following this equation:

  • display math(eqn 5)

During photosynthetic assimilation of CO2, plants discriminate against molecules of CO2 containing 13C because 13CO2 diffuses more slowly from the atmosphere to the site of carboxylation (stomatal diffusion) than does 12CO2. 13CO2 also reacts less with the primary carboxylating enzyme (Rubisco; Fig. 1). Farquhar, O'Leary & Berry (1982) showed that foliar carbon isotope composition (δ13C, ‰) is strongly negatively correlated with WUEint following this simplified equation:

  • display math(eqn 6)

where δ13Cair is the carbon isotope composition of the air, and a and b are factors characterising the discrimination against 13CO2 during stomatal diffusion and carboxylation, respectively. Therefore, δ13C provides a convenient time-integrated estimate of WUEint. Values for δ13C are obtained at the individual tree level by sampling representative subsets of leaves or needles, but individual values cannot simply be added to represent ecosystem-level carbon isotope composition (δ13Cplot). Instead, the contribution of a single tree to the carbon isotope composition of the whole population depends on tree-specific CO2 assimilation rates that control carbon isotope fractionation during photosynthesis (Lloyd & Farquhar 1994). Consequently, when δ13C values are scaled up from tree or species level to ecosystem level, tree or species δ13C values should be weighted by these assimilation rates (Fig. 2). Since direct measurements of CO2 assimilation rates cannot easily be made for each tree in the field, we used a convenient proxy for canopy-level, species CO2 assimilation. In a given environment, the quantum yield for reduction in end electron acceptors at the PSI acceptor side is strongly positively correlated with time-integrated leaf CO2 exchanges (Genty, Briantais & Baker 1989). Thus, the proportions of the measured quantum yield of species i can therefore be used as the weighting coefficient (WOi) for δ13C values.

image

Figure 1. Schematic representation of the processes involved in leaf carbon isotope discrimination during photosynthesis. The carbon isotope composition (δ13C) of total leaf organic matter is determined by the carbon isotope composition of CO2 in the air (δ13Cair) and the CO2 concentration in the air (Ca) and in the leaf intercellular spaces (Ci). Discrimination processes against 13CO2 occur during photosynthetic CO2 assimilation (A) when CO2 passes through the stomata (gs) from the outside air (fractionation factor a) and during the carboxylation process by the Rubisco enzyme inside the chloroplasts (fractionation factor b). The plain arrow represents A and the dotted arrow represents the transpiration flux.

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image

Figure 2. Comparison of the factors taken into account to calculate the observed trait at plot level for yield (YO) and carbon isotope composition (FO). For yield, the observed biomass of each species i in the mixture (BOi) and the proportion of each species in the mixture (pi) are taken into account to calculate YO. For carbon isotope composition, FO is dependent on the observed carbon isotope composition of species i in the mixture (δ13COi, i.e. FOi) and the corresponding CO2 assimilation rate during photosynthesis (Ai) representing the species-specific contribution to plot level carbon isotope composition. Letters on the trees denote different species.

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Materials

  1. Top of page
  2. Summary
  3. Introduction
  4. Application of Loreau & Hector's (2001) method to complex functional traits
  5. Application of the modified equations to ecosystem-level carbon isotope composition
  6. Materials
  7. Results and discussion
  8. Conclusion
  9. Acknowledgements
  10. Author contributions
  11. References

We conducted our study at the BIOTREE tree biodiversity experimental site in Germany (Kaltenborn site, Scherer-Lorenzen et al. 2007), which was planted in winter 2003–2004. This plantation is located on acidic sandy soils and includes four species: Fagus sylvatica (L.), Quercus petraea (Matt.), Picea abies (L.) Karst. and Pseudotsuga menziesii (Mirb.) Franco. The plantation was designed to assure maximum above- and below-ground interactions among species at the adult stage. Therefore, in the mixed plots of 120 × 48 m, each species was planted in monospecific rectangular patches of 8 × 8 m, arranged in a regular pattern in order to reduce out-competition of slow-growing species at an early stage and to maximise interspecific interactions along borders and corners (Scherer-Lorenzen et al. 2007). In summer 2011, we sampled leaves and needles from four trees per species and per plot in monocultures (n = four plots), two-species mixtures (n = 6), three-species mixtures (n = 4) and four-species mixtures (n = 1). In each plot, we only took samples from trees at the corners of the patches. The samples were oven-dried at 60°C for 48 h, then finely ground. δ13C analysis was carried out at the Stable Isotope Facility of UC Davis, USA. The δ13C (‰) values are expressed relative to the Vienna Pee Dee Belemnite standard. The quantum yield for reduction in end electron acceptors at the PSI acceptor side was measured with a HandyPea fluorimeter (Hansatech Instruments, Pentney-Norfolk, UK) on leaves or needles in close vicinity to the ones harvested for elemental and isotope analyses following the procedure described by Strasser et al. (2010). This value was then used as a weighting coefficient (WOi) when calculating biodiversity effects on δ13Cplot. We used the nonparametric Wilcoxon test to check for complementarity, selection and net effects among mixture levels and t-tests to evaluate whether all the indices differed significantly from zero (SAS 9.3; SAS Institute, Cary, NC, USA).

Results and discussion

  1. Top of page
  2. Summary
  3. Introduction
  4. Application of Loreau & Hector's (2001) method to complex functional traits
  5. Application of the modified equations to ecosystem-level carbon isotope composition
  6. Materials
  7. Results and discussion
  8. Conclusion
  9. Acknowledgements
  10. Author contributions
  11. References

We found large differences in ΔF, CE and SE among plots, with either positive or negative values (Fig. 3, Table 2). Positive or negative values confirmed that in this plantation, interactions among species drive δ13Cplot, and thus WUEplot. When considering individual species richness levels, we found that both the net effect and CE were significantly different from zero (< 0·05) for the two-species mixtures; however, we found no SE (= 0·27). Furthermore, the net effect and CE were mostly negative, suggesting lower observed δ13Cplot than what would have been expected based on the monoculture values. Since δ13C and water use efficiency are positively related (Farquhar, O'Leary & Berry 1982), our findings point towards lower WUEplot when several different species coexist. This result contrasts with previous patterns of enhanced water use efficiency found in species mixtures (Forrester et al. 2010; Kunert et al. 2012).

Table 2. Mean species foliar carbon isotope composition measured in the mixed plots (FOi, ‰), expected mean species foliar carbon isotope composition measured in the monoculture plots (FEi, ‰) and proportional weighting coefficient (WOi) of species i, in each studied plot for the four studied species: Fagus sylvatica (Fs), Pseudotsuga menziesii (Pm), Quercus petraea (Qp) and Picea abies (Pa). Species richness, net biodiversity effect (ΔF), complementarity effect (CE), selection effect (SE) and calculated plot carbon isotope composition (FO) are shown for each plot
PlotRichness levelSpecies F Oi F Ei W Oi ΔF CESE F O
32Fs−28·46−28·820·460·260·263·11 × 10−3−26·99
Pm−25·74−25·910·54
62Qp−27·43−26·600·50−0·48−0·47−5·91 × 10−3−26·64
Pa−25·84−25·720·50
72Pm−26·36−25·910·51−0·52−0·52−7·38 × 10−4−26·77
Qp−27·19−26·600·49
102Pm−26·13−25·910·58−0·30−0·302·14 × 10−4−26·13
Pa−26·15−25·720·42
122Fs−28·99−28·820·41−0·52−0·531·59 × 10−2−28·02
Qp−27·36−26·600·59
162Fs−28·58−28·820·36−0·26−0·282·54 × 10−2−27·11
Pa−26·26−25·720·64
43Fs−28·60−28·820·25−0·22−0·241·61 × 10−2−27·06
Qp−26·73−26·600·39
Pa−26·35−25·720·36
53Fs−28·57−28·820·290·150·15−5·72 × 10−4−26·84
Pm−25·57−25·910·36
Qp−26·75−26·600·35
93Fs−28·82−28·820·27−0·07−0·073·58 × 10−3−26·70
Pm−25·70−25·910·34
Pa−26·09−25·720·39
153Pm−26·25−25·910·38−0·47−0·472·54 × 10−2−27·11
Qp−27·20−26·600·30
Pa−26·23−25·720·31
84Fs−28·92−28·820·18−0·03−0·02−3·15 × 10−3−26·61
Pm−25·24−25·910·25
Qp−26·95−26·600·30
Pa−26·00−25·720·27
image

Figure 3. Application of the adapted method to plot carbon isotope composition (δ13Cplot). Net, complementarity and selection effects calculated for δ13Cplot for the different richness levels. Asterisks denote significant differences from zero for each effect (t-test, *< 0·05).

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The absence of a significant SE on WUEplot indicates that the overall negative net biodiversity effect observed in the two-species mixtures was primarily driven by a CE. Our interpretation is that the species coexisting in the mixed plots are in direct competition for the same resources because they still share the same ecological niche at the early establishment stage (7 years after planting, at the time of our measurements). This competition most likely caused a decrease in the ratio between carbon acquisition and transpiration at the ecosystem level in the two-species mixtures. As no overshading was observed, the competition among species is presumably occurring below-ground. This assumption is consistent with the strong competition among fine roots observed by Lei, Scherer-Lorenzen & Bauhus (2012) in this plantation.

Furthermore, we did not observe any significant effect of richness level for any of the biodiversity effects (> 0·05). This indicates that the number of species competing for resources does not significantly affect the difference in δ13Cplot between observed and expected values. The δ13C value for a given species in the two-, three- and four-species mixtures did not greatly change.

Conclusion

  1. Top of page
  2. Summary
  3. Introduction
  4. Application of Loreau & Hector's (2001) method to complex functional traits
  5. Application of the modified equations to ecosystem-level carbon isotope composition
  6. Materials
  7. Results and discussion
  8. Conclusion
  9. Acknowledgements
  10. Author contributions
  11. References

Applying the version of Loreau & Hector's (2001) method to complex components of ecosystem functioning will provide important new practical applications as well as conceptual insights into functional biodiversity research. We have shown here that, with the appropriate weighting factors for specific, complex functional properties, the method can be applied to a broad range of functional properties, rather than to yield alone. In our case, we used the quantum yield for reduction in end electron acceptors at the PSI acceptor side as the weighting factor for ecosystem-level carbon isotope composition. This combination of weights and functions provides an estimate of intrinsic water use efficiency in mixed species plots. For other complex traits, the selection of the most pertinent weighting factor should make it possible to determine the contribution of each species to the studied ecosystem property. Some of the weighting factors may be difficult to measure precisely with currently available equipment, as in the case of CO2 assimilation rates in our study. Nevertheless, if appropriate measurements are not easily obtainable, proxies could be found that provide the same proportional contributions; modelling approaches may be of help in this case. In the young mixed temperate plantation in our study, complementarity rather than SE were the substantial drivers of plot water use efficiency. As the plantation ages and taller trees with broader root systems begin to compete for light and soil resources, CE might increase and SE might arise due to more frequent interspecific interactions. It will thus be interesting to follow the changes in the relative importance of these two components of net biodiversity effects for a multitude of ecological processes and functions.

Acknowledgements

  1. Top of page
  2. Summary
  3. Introduction
  4. Application of Loreau & Hector's (2001) method to complex functional traits
  5. Application of the modified equations to ecosystem-level carbon isotope composition
  6. Materials
  7. Results and discussion
  8. Conclusion
  9. Acknowledgements
  10. Author contributions
  11. References

We thank Laureline Bes De Berc for her considerable technical support in leaf or needle collection and grinding. We would like to acknowledge the anonymous reviewers who greatly contributed to the improvement in a previous version of this manuscript. The research leading to these results was done within the FunDivEUROPE project, receiving funding from the European Union Seventh Framework Programme (FP7/2007–2013) under grant agreement no 265171. We also acknowledge the participants of the BACCARA project (FP7/2007–2013, grant agreement 226299) who contributed to data acquisition at the Kaltenborn plantation. This work was supported by the French National Research Agency through the Laboratory of Excellence ARBRE (ANR-12-LABXARBRE-01). CG was supported by a grant from INRA Nancy in the framework of the FunDivEUROPE project.

Author contributions

  1. Top of page
  2. Summary
  3. Introduction
  4. Application of Loreau & Hector's (2001) method to complex functional traits
  5. Application of the modified equations to ecosystem-level carbon isotope composition
  6. Materials
  7. Results and discussion
  8. Conclusion
  9. Acknowledgements
  10. Author contributions
  11. References

CG and DB elaborated the adaptation of the method to complex functional traits. DB, AG1, AG2 and MSL designed the experimental study. DB, MP and AG1 performed the experimental work. CG, DB, AG1 and AG2 analysed the results. CG and DB wrote the first draft of this manuscript and all authors substantially contributed to revisions.

References

  1. Top of page
  2. Summary
  3. Introduction
  4. Application of Loreau & Hector's (2001) method to complex functional traits
  5. Application of the modified equations to ecosystem-level carbon isotope composition
  6. Materials
  7. Results and discussion
  8. Conclusion
  9. Acknowledgements
  10. Author contributions
  11. References
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